The importance of depth of field is really subjective, and of different importance to each particular photo. In general, you want the subject of your portrait to stand out from the background, so yes, shallow dof helps in that sense, but depending on your background, you might not need shallow dof, or want it. It's really up to you.

I'd go with what Digital Matt said. There's tons of ways to make portraits and everyone's "style" is different so if your going for one look over the other than DOF may come into play. IMO DOF is one of the cornerstones of photography so if I was forced to say yes or no, I'd go with yes since you have to think about DOF in every shot that you take.

I would have to say yes and maybe no. Hows that for being exact? In your traditional portrait photography, you are generally using a static style background. In this case, the DOF wouldn't be as much of a concern. The way its lighted and exposure would rate higher. But if you are trying to isolate someone for a portrait in not so formal of a setting, then DOF would have a bigger influence.

Like the others have said, it depends on the background. You want enough focus on the subject to make sure they stand out. In general I shoot with very narrow/shallow depth of field in my portrait work.

I think that many portraits are shot with a shallow DOF. It's an effective way to separate the subject from the background.

On the other hand, when I'm shooting an environmental portrait I often use a deep DOF because I want to get the details of the background (their home, work, school, etc...), which would add to the story.